Adding default parameters to embedded YouTube videos

We just tried a feature we've seldom used in Umbraco. When going with the embed grid editor (possibly also prop editor), a YouTube movie is embedded with width, height and the URL set.

However, we needed to add rel=0 to the querystring to avoid getting the "more like this" screen at the end of the video.
Adding it to the URL while embedding did nothing. (It was stripped)

After digging around a bit in the code, we discovered the EmbeddedMedia.config file (only used Umbraco 6 years, can't know every file).
Seemed to me that adding rel=0 as a key value to the youtube provider would have the provider add it to the final URL. But it didn't.

Is there any option to do this? We ended up just adding the HTML to an RTE, but would be really nice to just configure default YouTube behavior.

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